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Concise representations of regular languages by degree and probabilistic finite automata

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Abstract

Meyer and Fischer b][MF] proved that nondeterministic finite automata (NFA) can be exponentially more concise than deterministic finite automata (DFA) in their representations of regular languages. Several variants of that basic finite state machine model are now being used to analyze parallelism and to build real-time software systems [HL+]. Even though these variants can sometimes represent regular languages in a more concise manner than NFA, the underlying models fundamentally differ from NFA in how they operate. Degree automata [W] (DA), however, differ from NFA only in their acceptance criteria and accept only regular languages. We show here that DA are also exponentially more concise than NFA on some sequences of regular languages. We also show that the conciseness of probabilistic automata [R] with isolated cutpoints can be unbounded over DA and, concurrently, i.e., over the same sequence of languages, those DA can be exponentially more concise than NFA.

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Authors and Affiliations

  1. AT&T Bell Laboratories, 600 Mountain Avenue, 07974, Murray Hill, NJ, USA

    Chandra M. R. Kintala

  2. Pennsylvania State University, 16802, University Park, PA, USA

    Kong -Yee Pun

  3. Johann Wolfgang Goethe-Universität, Frankfurt, Federal Republic of Germany

    Detlef Wotschke

Authors
  1. Chandra M. R. Kintala
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  2. Kong -Yee Pun
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  3. Detlef Wotschke
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Additional information

Detlef Wotschke was supported in part by “Deutsche Forschungsgemeinschaft” under Grant No. Wo 334/2-1 and by “Stiftung Volkswagenwerk” under Grant No. II/62 325.

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Kintala, C.M.R., Pun, K.Y. & Wotschke, D. Concise representations of regular languages by degree and probabilistic finite automata. Math. Systems Theory 26, 379–395 (1993). https://doi.org/10.1007/BF01189856

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  • DOI: https://doi.org/10.1007/BF01189856

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